MM Mean is a clothing retailer with a 24-hour active call center. Based on the historical data it is known that 9 percent of the calls coming to the call center involve return of items (return calls). The rest of the calls (non-return calls) are associated with new orders, payments, customer complaints, etc. It is reasonable to assume that outcome of each call (a return call or not) to be independent of the other calls. Please use this information in answering the following questions. You can use R in all cases for probability computations, but in so doing please write down the corresponding R statements for the computations.

(a) If the call center receives 30 calls, what is the probability that there will be more than 3 return calls ?

(b) If the call center receives 30 calls, what is the expected number of non-return calls ?

(c) If we monitor all the incoming calls to the center, what is the probability that the call center will get 10 non-return calls before they get a return call ?

(d) What is the expected number of non-return calls before a return call is received ?

(e) What is the expected number of non-return calls before two return calls are received ?